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Re: A harmless and amusing bug
*To*: mathgroup at smc.vnet.net
*Subject*: [mg76314] Re: A harmless and amusing bug
*From*: Ray Koopman <koopman at sfu.ca>
*Date*: Sat, 19 May 2007 04:47:12 -0400 (EDT)
*References*: <f2jtne$cef$1@smc.vnet.net>
On May 18, 3:04 am, Fred Simons <f.h.sim... at tue.nl> wrote:
> I found this example in a very old notebook of mine and I do not
> remember if this has already been discussed in this group.
>
> The following seems to be a harmless and amusing bug. It happens both in
> Mathematica 5 and in Mathematica 6 under Windows.
>
> Execute the following command:
>
> y = x /. DSolve[x''[t]+ 2 x'[t]+ x[t]==Sin[t], x, t][[1]]
>
> Copy the result, paste it in the following command and execute.
>
> z =pasted result
>
> Obviously, y equals z. However,
>
> SameQ[y,z] --> False
>
> So here we have an example of two different Mathematica expressions with
> the property that on level 1 all subexpressions are equal:
>
> And @@ Table[y[[i]] === z[[i]], {i, 0,2}] --> True
>
> It also is an example of two different expressions that convert to the
> same string:
>
> Equal[ToString /@ {y,z}] --> True
>
> The expression y has more leaves than can be found at level -1, and
> anyway less than the number of leaves of the expression z:
>
> {LeafCount[#], Length[Level[#, {-1}, Heads->True]]}& /@ {y,z} -->
> {{27,25},{29,29}}
>
> Fred Simons
> Eindhoven University of Technology
In[7]:=
FullForm[y]
Out[7]//FullForm=
Function[List[t],
Plus[Times[Power[E,Times[-1,t]],C[1]],
Times[Power[E,Times[-1,t]],t,C[2]],
Times[Rational[-1,2],Cos[t]]]]
In[8]:=
FullForm[z]
Out[8]//FullForm=
Function[List[t],
Plus[Times[Power[E,Times[-1,t]],C[1]],
Times[Power[E,Times[-1,t]],t,C[2]],
Times[-1,Times[Cos[t],Power[2,-1]]]]]
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